# Bohr Quantium Condition

A particle of mass m is attracted to the origin by a force proportional to the distance from the origin F = -kr. Assume that it moves in circular orbit of radius r.

a) Use Newton's law to show that its kinetic energy 1/2mv^2 equals its potential energy 1/2kr^2.

b) Use Bohr quantum condition on the angular momentum (L = nh) to show that the allowed orbitals are given by r^2 - nh*sqrt(km)

c) Find the allowed energies and show that they can be written E_n = nhf where f is the frequency of revolution.

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:55 pm ad1c9bdddfhttps://brainmass.com/physics/angular-momentum/bohr-quantium-condition-18363

#### Solution Preview

a.)

Because, force

F = -k*r = - m*v^2/r = -m*r*w^2 (centripetal force) ......(1)

where, w is angular velocity (rad/s)

=> m*v^2 = k*r^2

=> K.E. = (1/2)*m*v^2 = (1/2)*k*r^2 --Proved

b.)

Because, ...

#### Solution Summary

The solution provides step-by-step workings, interspersed with explanatory notes, to showing that the various energies and angular momentums of the described particle can be written a certain way.